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Network Working Group                                           G. AlmesRequest for Comments: 2679                                  S. KalidindiCategory: Standards Track                                   M. Zekauskas                                             Advanced Network & Services                                                          September 1999A One-way Delay Metric for IPPM1. Status of this Memo   This document specifies an Internet standards track protocol for the   Internet community, and requests discussion and suggestions for   improvements.  Please refer to the current edition of the "Internet   Official Protocol Standards" (STD 1) for the standardization state   and status of this protocol.  Distribution of this memo is unlimited.Copyright Notice   Copyright (C) The Internet Society (1999).  All Rights Reserved.2. Introduction   This memo defines a metric for one-way delay of packets across   Internet paths.  It builds on notions introduced and discussed in the   IPPM Framework document,RFC 2330 [1]; the reader is assumed to be   familiar with that document.   This memo is intended to be parallel in structure to a companion   document for Packet Loss ("A One-way Packet Loss Metric for IPPM")   [2].   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this   document are to be interpreted as described inRFC 2119 [6].   AlthoughRFC 2119 was written with protocols in mind, the key words   are used in this document for similar reasons.  They are used to   ensure the results of measurements from two different implementations   are comparable, and to note instances when an implementation could   perturb the network.   The structure of the memo is as follows:   +  A 'singleton' analytic metric, called Type-P-One-way-Delay, will      be introduced to measure a single observation of one-way delay.Almes, et al.               Standards Track                     [Page 1]

RFC 2679            A One-way Delay Metric for IPPM       September 1999   +  Using this singleton metric, a 'sample', called Type-P-One-way-      Delay-Poisson-Stream, will be introduced to measure a sequence of      singleton delays measured at times taken from a Poisson process.   +  Using this sample, several 'statistics' of the sample will be      defined and discussed.   This progression from singleton to sample to statistics, with clear   separation among them, is important.   Whenever a technical term from the IPPM Framework document is first   used in this memo, it will be tagged with a trailing asterisk.  For   example, "term*" indicates that "term" is defined in the Framework.2.1. Motivation:   One-way delay of a Type-P* packet from a source host* to a   destination host is useful for several reasons:   +  Some applications do not perform well (or at all) if end-to-end      delay between hosts is large relative to some threshold value.   +  Erratic variation in delay makes it difficult (or impossible) to      support many real-time applications.   +  The larger the value of delay, the more difficult it is for      transport-layer protocols to sustain high bandwidths.   +  The minimum value of this metric provides an indication of the      delay due only to propagation and transmission delay.   +  The minimum value of this metric provides an indication of the      delay that will likely be experienced when the path* traversed is      lightly loaded.   +  Values of this metric above the minimum provide an indication of      the congestion present in the path.   The measurement of one-way delay instead of round-trip delay is   motivated by the following factors:   +  In today's Internet, the path from a source to a destination may      be different than the path from the destination back to the source      ("asymmetric paths"), such that different sequences of routers are      used for the forward and reverse paths.  Therefore round-trip      measurements actually measure the performance of two distinct      paths together.  Measuring each path independently highlights the      performance difference between the two paths which may traverseAlmes, et al.               Standards Track                     [Page 2]

RFC 2679            A One-way Delay Metric for IPPM       September 1999      different Internet service providers, and even radically different      types of networks (for example, research versus commodity      networks, or ATM versus packet-over-SONET).   +  Even when the two paths are symmetric, they may have radically      different performance characteristics due to asymmetric queueing.   +  Performance of an application may depend mostly on the performance      in one direction.  For example, a file transfer using TCP may      depend more on the performance in the direction that data flows,      rather than the direction in which acknowledgements travel.   +  In quality-of-service (QoS) enabled networks, provisioning in one      direction may be radically different than provisioning in the      reverse direction, and thus the QoS guarantees differ.  Measuring      the paths independently allows the verification of both      guarantees.   It is outside the scope of this document to say precisely how delay   metrics would be applied to specific problems.2.2. General Issues Regarding Time   {Comment: the terminology below differs from that defined by ITU-T   documents (e.g., G.810, "Definitions and terminology for   synchronization networks" and I.356, "B-ISDN ATM layer cell transfer   performance"), but is consistent with the IPPM Framework document.   In general, these differences derive from the different backgrounds;   the ITU-T documents historically have a telephony origin, while the   authors of this document (and the Framework) have a computer systems   background.  Although the terms defined below have no direct   equivalent in the ITU-T definitions, after our definitions we will   provide a rough mapping.  However, note one potential confusion: our   definition of "clock" is the computer operating systems definition   denoting a time-of-day clock, while the ITU-T definition of clock   denotes a frequency reference.}   Whenever a time (i.e., a moment in history) is mentioned here, it is   understood to be measured in seconds (and fractions) relative to UTC.   As described more fully in the Framework document, there are four   distinct, but related notions of clock uncertainty:Almes, et al.               Standards Track                     [Page 3]

RFC 2679            A One-way Delay Metric for IPPM       September 1999   synchronization*         measures the extent to which two clocks agree on what time it         is.  For example, the clock on one host might be 5.4 msec ahead         of the clock on a second host.  {Comment: A rough ITU-T         equivalent is "time error".}   accuracy*         measures the extent to which a given clock agrees with UTC.         For example, the clock on a host might be 27.1 msec behind UTC.         {Comment: A rough ITU-T equivalent is "time error from UTC".}   resolution*         measures the precision of a given clock.  For example, the         clock on an old Unix host might tick only once every 10 msec,         and thus have a resolution of only 10 msec.  {Comment: A very         rough ITU-T equivalent is "sampling period".}   skew*         measures the change of accuracy, or of synchronization, with         time.  For example, the clock on a given host might gain 1.3         msec per hour and thus be 27.1 msec behind UTC at one time and         only 25.8 msec an hour later.  In this case, we say that the         clock of the given host has a skew of 1.3 msec per hour         relative to UTC, which threatens accuracy.  We might also speak         of the skew of one clock relative to another clock, which         threatens synchronization.  {Comment: A rough ITU-T equivalent         is "time drift".}3. A Singleton Definition for One-way Delay3.1. Metric Name:   Type-P-One-way-Delay3.2. Metric Parameters:   +  Src, the IP address of a host   +  Dst, the IP address of a host   +  T, a timeAlmes, et al.               Standards Track                     [Page 4]

RFC 2679            A One-way Delay Metric for IPPM       September 19993.3. Metric Units:   The value of a Type-P-One-way-Delay is either a real number, or an   undefined (informally, infinite) number of seconds.3.4. Definition:   For a real number dT, >>the *Type-P-One-way-Delay* from Src to Dst at   T is dT<< means that Src sent the first bit of a Type-P packet to Dst   at wire-time* T and that Dst received the last bit of that packet at   wire-time T+dT.   >>The *Type-P-One-way-Delay* from Src to Dst at T is undefined   (informally, infinite)<< means that Src sent the first bit of a   Type-P packet to Dst at wire-time T and that Dst did not receive that   packet.   Suggestions for what to report along with metric values appear inSection 3.8 after a discussion of the metric, methodologies for   measuring the metric, and error analysis.3.5. Discussion:   Type-P-One-way-Delay is a relatively simple analytic metric, and one   that we believe will afford effective methods of measurement.   The following issues are likely to come up in practice:   +  Real delay values will be positive.  Therefore, it does not make      sense to report a negative value as a real delay.  However, an      individual zero or negative delay value might be useful as part of      a stream when trying to discover a distribution of a stream of      delay values.   +  Since delay values will often be as low as the 100 usec to 10 msec      range, it will be important for Src and Dst to synchronize very      closely.  GPS systems afford one way to achieve synchronization to      within several 10s of usec.  Ordinary application of NTP may allow      synchronization to within several msec, but this depends on the      stability and symmetry of delay properties among those NTP agents      used, and this delay is what we are trying to measure.  A      combination of some GPS-based NTP servers and a conservatively      designed and deployed set of other NTP servers should yield good      results, but this is yet to be tested.   +  A given methodology will have to include a way to determine      whether a delay value is infinite or whether it is merely very      large (and the packet is yet to arrive at Dst).  As noted byAlmes, et al.               Standards Track                     [Page 5]

RFC 2679            A One-way Delay Metric for IPPM       September 1999      Mahdavi and Paxson [4], simple upper bounds (such as the 255      seconds theoretical upper bound on the lifetimes of IP packets      [5]) could be used, but good engineering, including an      understanding of packet lifetimes, will be needed in practice.      {Comment: Note that, for many applications of these metrics, the      harm in treating a large delay as infinite might be zero or very      small.  A TCP data packet, for example, that arrives only after      several multiples of the RTT may as well have been lost.}   +  If the packet is duplicated along the path (or paths) so that      multiple non-corrupt copies arrive at the destination, then the      packet is counted as received, and the first copy to arrive      determines the packet's one-way delay.   +  If the packet is fragmented and if, for whatever reason,      reassembly does not occur, then the packet will be deemed lost.3.6. Methodologies:   As with other Type-P-* metrics, the detailed methodology will depend   on the Type-P (e.g., protocol number, UDP/TCP port number, size,   precedence).   Generally, for a given Type-P, the methodology would proceed as   follows:   +  Arrange that Src and Dst are synchronized; that is, that they have      clocks that are very closely synchronized with each other and each      fairly close to the actual time.   +  At the Src host, select Src and Dst IP addresses, and form a test      packet of Type-P with these addresses.  Any 'padding' portion of      the packet needed only to make the test packet a given size should      be filled with randomized bits to avoid a situation in which the      measured delay is lower than it would otherwise be due to      compression techniques along the path.   +  At the Dst host, arrange to receive the packet.   +  At the Src host, place a timestamp in the prepared Type-P packet,      and send it towards Dst.   +  If the packet arrives within a reasonable period of time, take a      timestamp as soon as possible upon the receipt of the packet.  By      subtracting the two timestamps, an estimate of one-way delay can      be computed.  Error analysis of a given implementation of the      method must take into account the closeness of synchronization      between Src and Dst.  If the delay between Src's timestamp and theAlmes, et al.               Standards Track                     [Page 6]

RFC 2679            A One-way Delay Metric for IPPM       September 1999      actual sending of the packet is known, then the estimate could be      adjusted by subtracting this amount; uncertainty in this value      must be taken into account in error analysis.  Similarly, if the      delay between the actual receipt of the packet and Dst's timestamp      is known, then the estimate could be adjusted by subtracting this      amount; uncertainty in this value must be taken into account in      error analysis.  See the next section, "Errors and Uncertainties",      for a more detailed discussion.   +  If the packet fails to arrive within a reasonable period of time,      the one-way delay is taken to be undefined (informally, infinite).      Note that the threshold of 'reasonable' is a parameter of the      methodology.   Issues such as the packet format, the means by which Dst knows when   to expect the test packet, and the means by which Src and Dst are   synchronized are outside the scope of this document.  {Comment: We   plan to document elsewhere our own work in describing such more   detailed implementation techniques and we encourage others to as   well.}3.7. Errors and Uncertainties:   The description of any specific measurement method should include an   accounting and analysis of various sources of error or uncertainty.   The Framework document provides general guidance on this point, but   we note here the following specifics related to delay metrics:   +  Errors or uncertainties due to uncertainties in the clocks of the      Src and Dst hosts.   +  Errors or uncertainties due to the difference between 'wire time'      and 'host time'.   In addition, the loss threshold may affect the results.  Each of   these are discussed in more detail below, along with a section   ("Calibration") on accounting for these errors and uncertainties.3.7.1. Errors or uncertainties related to Clocks   The uncertainty in a measurement of one-way delay is related, in   part, to uncertainties in the clocks of the Src and Dst hosts.  In   the following, we refer to the clock used to measure when the packet   was sent from Src as the source clock, we refer to the clock used to   measure when the packet was received by Dst as the destination clock,   we refer to the observed time when the packet was sent by the source   clock as Tsource, and the observed time when the packet was received   by the destination clock as Tdest.  Alluding to the notions ofAlmes, et al.               Standards Track                     [Page 7]

RFC 2679            A One-way Delay Metric for IPPM       September 1999   synchronization, accuracy, resolution, and skew mentioned in the   Introduction, we note the following:   +  Any error in the synchronization between the source clock and the      destination clock will contribute to error in the delay      measurement.  We say that the source clock and the destination      clock have a synchronization error of Tsynch if the source clock      is Tsynch ahead of the destination clock.  Thus, if we know the      value of Tsynch exactly, we could correct for clock      synchronization by adding Tsynch to the uncorrected value of      Tdest-Tsource.   +  The accuracy of a clock is important only in identifying the time      at which a given delay was measured.  Accuracy, per se, has no      importance to the accuracy of the measurement of delay.  When      computing delays, we are interested only in the differences      between clock values, not the values themselves.   +  The resolution of a clock adds to uncertainty about any time      measured with it.  Thus, if the source clock has a resolution of      10 msec, then this adds 10 msec of uncertainty to any time value      measured with it.  We will denote the resolution of the source      clock and the destination clock as Rsource and Rdest,      respectively.   +  The skew of a clock is not so much an additional issue as it is a      realization of the fact that Tsynch is itself a function of time.      Thus, if we attempt to measure or to bound Tsynch, this needs to      be done periodically.  Over some periods of time, this function      can be approximated as a linear function plus some higher order      terms; in these cases, one option is to use knowledge of the      linear component to correct the clock.  Using this correction, the      residual Tsynch is made smaller, but remains a source of      uncertainty that must be accounted for.  We use the function      Esynch(t) to denote an upper bound on the uncertainty in      synchronization.  Thus, |Tsynch(t)| <= Esynch(t).   Taking these items together, we note that naive computation Tdest-   Tsource will be off by Tsynch(t) +/- (Rsource + Rdest).  Using the   notion of Esynch(t), we note that these clock-related problems   introduce a total uncertainty of Esynch(t)+ Rsource + Rdest.  This   estimate of total clock-related uncertainty should be included in the   error/uncertainty analysis of any measurement implementation.Almes, et al.               Standards Track                     [Page 8]

RFC 2679            A One-way Delay Metric for IPPM       September 19993.7.2. Errors or uncertainties related to Wire-time vs Host-time   As we have defined one-way delay, we would like to measure the time   between when the test packet leaves the network interface of Src and   when it (completely) arrives at the network interface of Dst, and we   refer to these as "wire times."  If the timings are themselves   performed by software on Src and Dst, however, then this software can   only directly measure the time between when Src grabs a timestamp   just prior to sending the test packet and when Dst grabs a timestamp   just after having received the test packet, and we refer to these two   points as "host times".   To the extent that the difference between wire time and host time is   accurately known, this knowledge can be used to correct for host time   measurements and the corrected value more accurately estimates the   desired (wire time) metric.   To the extent, however, that the difference between wire time and   host time is uncertain, this uncertainty must be accounted for in an   analysis of a given measurement method.  We denote by Hsource an   upper bound on the uncertainty in the difference between wire time   and host time on the Src host, and similarly define Hdest for the Dst   host.  We then note that these problems introduce a total uncertainty   of Hsource+Hdest.  This estimate of total wire-vs-host uncertainty   should be included in the error/uncertainty analysis of any   measurement implementation.3.7.3. Calibration   Generally, the measured values can be decomposed as follows:      measured value = true value + systematic error + random error   If the systematic error (the constant bias in measured values) can be   determined, it can be compensated for in the reported results.      reported value = measured value - systematic error   therefore      reported value = true value + random error   The goal of calibration is to determine the systematic and random   error generated by the instruments themselves in as much detail as   possible.  At a minimum, a bound ("e") should be found such that the   reported value is in the range (true value - e) to (true value + e)   at least 95 percent of the time.  We call "e" the calibration error   for the measurements.  It represents the degree to which the valuesAlmes, et al.               Standards Track                     [Page 9]

RFC 2679            A One-way Delay Metric for IPPM       September 1999   produced by the measurement instrument are repeatable; that is, how   closely an actual delay of 30 ms is reported as 30 ms.  {Comment: 95   percent was chosen because (1) some confidence level is desirable to   be able to remove outliers, which will be found in measuring any   physical property; (2) a particular confidence level should be   specified so that the results of independent implementations can be   compared; and (3) even with a prototype user-level implementation,   95% was loose enough to exclude outliers.}   From the discussion in the previous two sections, the error in   measurements could be bounded by determining all the individual   uncertainties, and adding them together to form       Esynch(t) + Rsource + Rdest + Hsource + Hdest.   However, reasonable bounds on both the clock-related uncertainty   captured by the first three terms and the host-related uncertainty   captured by the last two terms should be possible by careful design   techniques and calibrating the instruments using a known, isolated,   network in a lab.   For example, the clock-related uncertainties are greatly reduced   through the use of a GPS time source.  The sum of Esynch(t) + Rsource   + Rdest is small, and is also bounded for the duration of the   measurement because of the global time source.   The host-related uncertainties, Hsource + Hdest, could be bounded by   connecting two instruments back-to-back with a high-speed serial link   or isolated LAN segment.  In this case, repeated measurements are   measuring the same one-way delay.   If the test packets are small, such a network connection has a   minimal delay that may be approximated by zero.  The measured delay   therefore contains only systematic and random error in the   instrumentation.  The "average value" of repeated measurements is the   systematic error, and the variation is the random error.   One way to compute the systematic error, and the random error to a   95% confidence is to repeat the experiment many times - at least   hundreds of tests.  The systematic error would then be the median.   The random error could then be found by removing the systematic error   from the measured values.  The 95% confidence interval would be the   range from the 2.5th percentile to the 97.5th percentile of these   deviations from the true value.  The calibration error "e" could then   be taken to be the largest absolute value of these two numbers, plus   the clock-related uncertainty.  {Comment: as described, this bound is   relatively loose since the uncertainties are added, and the absolute   value of the largest deviation is used.  As long as the resultingAlmes, et al.               Standards Track                    [Page 10]

RFC 2679            A One-way Delay Metric for IPPM       September 1999   value is not a significant fraction of the measured values, it is a   reasonable bound.  If the resulting value is a significant fraction   of the measured values, then more exact methods will be needed to   compute the calibration error.}   Note that random error is a function of measurement load.  For   example, if many paths will be measured by one instrument, this might   increase interrupts, process scheduling, and disk I/O (for example,   recording the measurements), all of which may increase the random   error in measured singletons.  Therefore, in addition to minimal load   measurements to find the systematic error, calibration measurements   should be performed with the same measurement load that the   instruments will see in the field.   We wish to reiterate that this statistical treatment refers to the   calibration of the instrument; it is used to "calibrate the meter   stick" and say how well the meter stick reflects reality.   In addition to calibrating the instruments for finite one-way delay,   two checks should be made to ensure that packets reported as losses   were really lost.  First, the threshold for loss should be verified.   In particular, ensure the "reasonable" threshold is reasonable: that   it is very unlikely a packet will arrive after the threshold value,   and therefore the number of packets lost over an interval is not   sensitive to the error bound on measurements.  Second, consider the   possibility that a packet arrives at the network interface, but is   lost due to congestion on that interface or to other resource   exhaustion (e.g. buffers) in the instrument.3.8. Reporting the metric:   The calibration and context in which the metric is measured MUST be   carefully considered, and SHOULD always be reported along with metric   results.  We now present four items to consider: the Type-P of test   packets, the threshold of infinite delay (if any), error calibration,   and the path traversed by the test packets.  This list is not   exhaustive; any additional information that could be useful in   interpreting applications of the metrics should also be reported.3.8.1. Type-P   As noted in the Framework document [1], the value of the metric may   depend on the type of IP packets used to make the measurement, or   "type-P".  The value of Type-P-One-way-Delay could change if the   protocol (UDP or TCP), port number, size, or arrangement for special   treatment (e.g., IP precedence or RSVP) changes.  The exact Type-P   used to make the measurements MUST be accurately reported.Almes, et al.               Standards Track                    [Page 11]

RFC 2679            A One-way Delay Metric for IPPM       September 19993.8.2. Loss threshold   In addition, the threshold (or methodology to distinguish) between a   large finite delay and loss MUST be reported.3.8.3. Calibration results   +  If the systematic error can be determined, it SHOULD be removed      from the measured values.   +  You SHOULD also report the calibration error, e, such that the      true value is the reported value plus or minus e, with 95%      confidence (see the last section.)   +  If possible, the conditions under which a test packet with finite      delay is reported as lost due to resource exhaustion on the      measurement instrument SHOULD be reported.3.8.4. Path   Finally, the path traversed by the packet SHOULD be reported, if   possible.  In general it is impractical to know the precise path a   given packet takes through the network.  The precise path may be   known for certain Type-P on short or stable paths.  If Type-P   includes the record route (or loose-source route) option in the IP   header, and the path is short enough, and all routers* on the path   support record (or loose-source) route, then the path will be   precisely recorded.  This is impractical because the route must be   short enough, many routers do not support (or are not configured for)   record route, and use of this feature would often artificially worsen   the performance observed by removing the packet from common-case   processing.  However, partial information is still valuable context.   For example, if a host can choose between two links* (and hence two   separate routes from Src to Dst), then the initial link used is   valuable context.  {Comment: For example, with Merit's NetNow setup,   a Src on one NAP can reach a Dst on another NAP by either of several   different backbone networks.}4. A Definition for Samples of One-way Delay   Given the singleton metric Type-P-One-way-Delay, we now define one   particular sample of such singletons.  The idea of the sample is to   select a particular binding of the parameters Src, Dst, and Type-P,   then define a sample of values of parameter T.  The means for   defining the values of T is to select a beginning time T0, a final   time Tf, and an average rate lambda, then define a pseudo-randomAlmes, et al.               Standards Track                    [Page 12]

RFC 2679            A One-way Delay Metric for IPPM       September 1999   Poisson process of rate lambda, whose values fall between T0 and Tf.   The time interval between successive values of T will then average   1/lambda.   {Comment: Note that Poisson sampling is only one way of defining a   sample.  Poisson has the advantage of limiting bias, but other   methods of sampling might be appropriate for different situations.   We encourage others who find such appropriate cases to use this   general framework and submit their sampling method for   standardization.}4.1. Metric Name:   Type-P-One-way-Delay-Poisson-Stream4.2. Metric Parameters:   +  Src, the IP address of a host   +  Dst, the IP address of a host   +  T0, a time   +  Tf, a time   +  lambda, a rate in reciprocal seconds4.3. Metric Units:   A sequence of pairs; the elements of each pair are:   +  T, a time, and   +  dT, either a real number or an undefined number of seconds.   The values of T in the sequence are monotonic increasing.  Note that   T would be a valid parameter to Type-P-One-way-Delay, and that dT   would be a valid value of Type-P-One-way-Delay.4.4. Definition:   Given T0, Tf, and lambda, we compute a pseudo-random Poisson process   beginning at or before T0, with average arrival rate lambda, and   ending at or after Tf.  Those time values greater than or equal to T0   and less than or equal to Tf are then selected.  At each of the times   in this process, we obtain the value of Type-P-One-way-Delay at this   time.  The value of the sample is the sequence made up of the   resulting <time, delay> pairs.  If there are no such pairs, theAlmes, et al.               Standards Track                    [Page 13]

RFC 2679            A One-way Delay Metric for IPPM       September 1999   sequence is of length zero and the sample is said to be empty.4.5. Discussion:   The reader should be familiar with the in-depth discussion of Poisson   sampling in the Framework document [1], which includes methods to   compute and verify the pseudo-random Poisson process.   We specifically do not constrain the value of lambda, except to note   the extremes.  If the rate is too large, then the measurement traffic   will perturb the network, and itself cause congestion.  If the rate   is too small, then you might not capture interesting network   behavior.  {Comment: We expect to document our experiences with, and   suggestions for, lambda elsewhere, culminating in a "best current   practices" document.}   Since a pseudo-random number sequence is employed, the sequence of   times, and hence the value of the sample, is not fully specified.   Pseudo-random number generators of good quality will be needed to   achieve the desired qualities.   The sample is defined in terms of a Poisson process both to avoid the   effects of self-synchronization and also capture a sample that is   statistically as unbiased as possible.  {Comment: there is, of   course, no claim that real Internet traffic arrives according to a   Poisson arrival process.}  The Poisson process is used to schedule   the delay measurements.  The test packets will generally not arrive   at Dst according to a Poisson distribution, since they are influenced   by the network.   All the singleton Type-P-One-way-Delay metrics in the sequence will   have the same values of Src, Dst, and Type-P.   Note also that, given one sample that runs from T0 to Tf, and given   new time values T0' and Tf' such that T0 <= T0' <= Tf' <= Tf, the   subsequence of the given sample whose time values fall between T0'   and Tf' are also a valid Type-P-One-way-Delay-Poisson-Stream sample.4.6. Methodologies:   The methodologies follow directly from:   +  the selection of specific times, using the specified Poisson      arrival process, and   +  the methodologies discussion already given for the singleton      Type-P-One-way-Delay metric.Almes, et al.               Standards Track                    [Page 14]

RFC 2679            A One-way Delay Metric for IPPM       September 1999   Care must, of course, be given to correctly handle out-of-order   arrival of test packets; it is possible that the Src could send one   test packet at TS[i], then send a second one (later) at TS[i+1],   while the Dst could receive the second test packet at TR[i+1], and   then receive the first one (later) at TR[i].4.7. Errors and Uncertainties:   In addition to sources of errors and uncertainties associated with   methods employed to measure the singleton values that make up the   sample, care must be given to analyze the accuracy of the Poisson   process with respect to the wire-times of the sending of the test   packets.  Problems with this process could be caused by several   things, including problems with the pseudo-random number techniques   used to generate the Poisson arrival process, or with jitter in the   value of Hsource (mentioned above as uncertainty in the singleton   delay metric).  The Framework document shows how to use the   Anderson-Darling test to verify the accuracy of a Poisson process   over small time frames.  {Comment: The goal is to ensure that test   packets are sent "close enough" to a Poisson schedule, and avoid   periodic behavior.}4.8. Reporting the metric:   You MUST report the calibration and context for the underlying   singletons along with the stream.  (See "Reporting the metric" for   Type-P-One-way-Delay.)5. Some Statistics Definitions for One-way Delay   Given the sample metric Type-P-One-way-Delay-Poisson-Stream, we now   offer several statistics of that sample.  These statistics are   offered mostly to be illustrative of what could be done.5.1. Type-P-One-way-Delay-Percentile   Given a Type-P-One-way-Delay-Poisson-Stream and a percent X between   0% and 100%, the Xth percentile of all the dT values in the Stream.   In computing this percentile, undefined values are treated as   infinitely large.  Note that this means that the percentile could   thus be undefined (informally, infinite).  In addition, the Type-P-   One-way-Delay-Percentile is undefined if the sample is empty.Almes, et al.               Standards Track                    [Page 15]

RFC 2679            A One-way Delay Metric for IPPM       September 1999   Example: suppose we take a sample and the results are:      Stream1 = <      <T1, 100 msec>      <T2, 110 msec>      <T3, undefined>      <T4, 90 msec>      <T5, 500 msec>      >   Then the 50th percentile would be 110 msec, since 90 msec and 100   msec are smaller and 110 msec and 'undefined' are larger.   Note that if the possibility that a packet with finite delay is   reported as lost is significant, then a high percentile (90th or   95th) might be reported as infinite instead of finite.5.2. Type-P-One-way-Delay-Median   Given a Type-P-One-way-Delay-Poisson-Stream, the median of all the dT   values in the Stream.  In computing the median, undefined values are   treated as infinitely large.  As with Type-P-One-way-Delay-   Percentile, Type-P-One-way-Delay-Median is undefined if the sample is   empty.   As noted in the Framework document, the median differs from the 50th   percentile only when the sample contains an even number of values, in   which case the mean of the two central values is used.   Example: suppose we take a sample and the results are:   Stream2 = <      <T1, 100 msec>      <T2, 110 msec>      <T3, undefined>      <T4, 90 msec>      >   Then the median would be 105 msec, the mean of 100 msec and 110 msec,   the two central values.5.3. Type-P-One-way-Delay-Minimum   Given a Type-P-One-way-Delay-Poisson-Stream, the minimum of all the   dT values in the Stream.    In computing this, undefined values are   treated as infinitely large.  Note that this means that the minimum   could thus be undefined (informally, infinite) if all the dT values   are undefined.  In addition, the Type-P-One-way-Delay-Minimum isAlmes, et al.               Standards Track                    [Page 16]

RFC 2679            A One-way Delay Metric for IPPM       September 1999   undefined if the sample is empty.   In the above example, the minimum would be 90 msec.5.4. Type-P-One-way-Delay-Inverse-Percentile   Given a Type-P-One-way-Delay-Poisson-Stream and a time duration   threshold, the fraction of all the dT values in the Stream less than   or equal to the threshold.  The result could be as low as 0% (if all   the dT values exceed threshold) or as high as 100%.  Type-P-One-way-   Delay-Inverse-Percentile is undefined if the sample is empty.   In the above example, the Inverse-Percentile of 103 msec would be   50%.6. Security Considerations   Conducting Internet measurements raises both security and privacy   concerns.  This memo does not specify an implementation of the   metrics, so it does not directly affect the security of the Internet   nor of applications which run on the Internet.  However,   implementations of these metrics must be mindful of security and   privacy concerns.   There are two types of security concerns: potential harm caused by   the measurements, and potential harm to the measurements.  The   measurements could cause harm because they are active, and inject   packets into the network.  The measurement parameters MUST be   carefully selected so that the measurements inject trivial amounts of   additional traffic into the networks they measure.  If they inject   "too much" traffic, they can skew the results of the measurement, and   in extreme cases cause congestion and denial of service.   The measurements themselves could be harmed by routers giving   measurement traffic a different priority than "normal" traffic, or by   an attacker injecting artificial measurement traffic.  If routers can   recognize measurement traffic and treat it separately, the   measurements will not reflect actual user traffic.  If an attacker   injects artificial traffic that is accepted as legitimate, the loss   rate will be artificially lowered.  Therefore, the measurement   methodologies SHOULD include appropriate techniques to reduce the   probability measurement traffic can be distinguished from "normal"   traffic.  Authentication techniques, such as digital signatures, may   be used where appropriate to guard against injected traffic attacks.   The privacy concerns of network measurement are limited by the active   measurements described in this memo.  Unlike passive measurements,   there can be no release of existing user data.Almes, et al.               Standards Track                    [Page 17]

RFC 2679            A One-way Delay Metric for IPPM       September 19997. Acknowledgements   Special thanks are due to Vern Paxson of Lawrence Berkeley Labs for   his helpful comments on issues of clock uncertainty and statistics.   Thanks also to Garry Couch, Will Leland, Andy Scherrer, Sean Shapira,   and Roland Wittig for several useful suggestions.8. References   [1]  Paxson, V., Almes, G., Mahdavi, J. and M. Mathis, "Framework for        IP Performance Metrics",RFC 2330, May 1998.   [2]  Almes, G., Kalidindi, S. and M. Zekauskas, "A One-way Packet        Loss Metric for IPPM",RFC 2680, September 1999.   [3]  Mills, D., "Network Time Protocol (v3)",RFC 1305, April 1992.   [4]  Mahdavi J. and V. Paxson, "IPPM Metrics for Measuring        Connectivity",RFC 2678, September 1999.   [5]  Postel, J., "Internet Protocol", STD 5,RFC 791, September 1981.   [6]  Bradner, S., "Key words for use in RFCs to Indicate Requirement        Levels",BCP 14,RFC 2119, March 1997.   [7]  Bradner, S., "The Internet Standards Process -- Revision 3",BCP9,RFC 2026, October 1996.Almes, et al.               Standards Track                    [Page 18]

RFC 2679            A One-way Delay Metric for IPPM       September 19999. Authors' Addresses   Guy Almes   Advanced Network & Services, Inc.   200 Business Park Drive   Armonk, NY  10504   USA   Phone: +1 914 765 1120   EMail: almes@advanced.org   Sunil Kalidindi   Advanced Network & Services, Inc.   200 Business Park Drive   Armonk, NY  10504   USA   Phone: +1 914 765 1128   EMail: kalidindi@advanced.org   Matthew J. Zekauskas   Advanced Network & Services, Inc.   200 Business Park Drive   Armonk, NY 10504   USA   Phone: +1 914 765 1112   EMail: matt@advanced.orgAlmes, et al.               Standards Track                    [Page 19]

RFC 2679            A One-way Delay Metric for IPPM       September 199910.  Full Copyright Statement   Copyright (C) The Internet Society (1999).  All Rights Reserved.   This document and translations of it may be copied and furnished to   others, and derivative works that comment on or otherwise explain it   or assist in its implementation may be prepared, copied, published   and distributed, in whole or in part, without restriction of any   kind, provided that the above copyright notice and this paragraph are   included on all such copies and derivative works.  However, this   document itself may not be modified in any way, such as by removing   the copyright notice or references to the Internet Society or other   Internet organizations, except as needed for the purpose of   developing Internet standards in which case the procedures for   copyrights defined in the Internet Standards process must be   followed, or as required to translate it into languages other than   English.   The limited permissions granted above are perpetual and will not be   revoked by the Internet Society or its successors or assigns.   This document and the information contained herein is provided on an   "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING   TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING   BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION   HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF   MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.Acknowledgement   Funding for the RFC Editor function is currently provided by the   Internet Society.Almes, et al.               Standards Track                    [Page 20]